Issue 45, 2020

Solving complex eigenvalue problems on a quantum annealer with applications to quantum scattering resonances

Abstract

Quantum computing is a new and rapidly evolving paradigm for solving chemistry problems. In previous work, we developed the Quantum Annealer Eigensolver (QAE) and applied it to the calculation of the vibrational spectrum of a molecule on the D-Wave quantum annealer. However, the original QAE methodology was applicable to real symmetric matrices only. For many physics and chemistry problems, the diagonalization of complex matrices is required. For example, the calculation of quantum scattering resonances can be formulated as a complex eigenvalue problem where the real part of the eigenvalue is the resonance energy and the imaginary part is proportional to the resonance width. In the present work, we generalize the QAE to treat complex matrices: first complex Hermitian matrices and then complex symmetric matrices. These generalizations are then used to compute a quantum scattering resonance state in a 1D model potential for O + O collisions. These calculations are performed using both a software (classical) annealer and hardware annealer (the D-Wave 2000Q). The results of the complex QAE are also benchmarked against a standard linear algebra library (LAPACK). This work presents the first numerical solution of a complex eigenvalue problem of any kind on a quantum annealer, and it is the first treatment of a quantum scattering resonance on any quantum device.

Graphical abstract: Solving complex eigenvalue problems on a quantum annealer with applications to quantum scattering resonances

Article information

Article type
Paper
Submitted
11 ágú. 2020
Accepted
29 sep. 2020
First published
02 okt. 2020

Phys. Chem. Chem. Phys., 2020,22, 26136-26144

Author version available

Solving complex eigenvalue problems on a quantum annealer with applications to quantum scattering resonances

A. Teplukhin, B. K. Kendrick and D. Babikov, Phys. Chem. Chem. Phys., 2020, 22, 26136 DOI: 10.1039/D0CP04272B

To request permission to reproduce material from this article, please go to the Copyright Clearance Center request page.

If you are an author contributing to an RSC publication, you do not need to request permission provided correct acknowledgement is given.

If you are the author of this article, you do not need to request permission to reproduce figures and diagrams provided correct acknowledgement is given. If you want to reproduce the whole article in a third-party publication (excluding your thesis/dissertation for which permission is not required) please go to the Copyright Clearance Center request page.

Read more about how to correctly acknowledge RSC content.

Social activity

Spotlight

Advertisements